Revisiting Network Value: Sublinear Knowledge Law

Abstract: Three influential laws, namely Sarnoff's Law, Metcalfe's Law, and Reed's Law, have been established to describe network value in terms of the number of neighbors, edges, and subgraphs. Here, we highlight the coexistence of these laws in citation networks for the first time, utilizing the Deep-time Digital Earth academic literature. We further introduce a novel concept called the sublinear knowledge law, which demonstrates that knowledge growth is notably slower than both the growth rate of network size and the rates outlined by the aforementioned traditional laws. These results offer an innovative perspective while also filling a gap regarding network value.